Prove that `(-a,-a/2)` is the orthocentre of the triangle formed by the lines ` y = m_(i) x + a/(m_(i)) , I = 1,2,3, m_(1) m_(2) m_(3) ` being the roots of the equation `x^(3) - 3x^(2) + 2 = 0 `

Show that the area of the triangle formed buy the lines y=m_1x , y=m_2x\ a n d\ y=c is equal to (c^2)/4(sqrt(33)+sqrt(11))w h e r e\ m_1,\ m_2 are the roots of the equation x ^2+(sqrt(3)+2)x+sqrt(3)-1=0.

The quadratic equation x^(2) - (m -3)x + m =0 has

Show that the area of the triangle formed by the lines y=m_1x+c_1,""""y=m_2x+c_2 and x=0 is ((c_1-c_2)^2)/(2|m_1-m_2|)

Show that the area of the triangle formed by the lines y=m_1x+c_1,""""y=m_2x+c_2 and x=0 is ((c_1-c_2)^2)/(2|m_1-m_2|)

If m_(1),m_(2) be the roots of the equation x^(2)+(sqrt(3)+2)x+sqrt(3)-1 =0 , then the area of the triangle formed by the lines y = m_(1)x,y = m_(2)x and y = 2 is

If m_1 and m_2 are roots of equation x^2+(sqrt(3)+2)x+sqrt(3)-1=0 the the area of the triangle formed by lines y=m_1x, y = m_2x, y=c is:

Solve the equation x^3 -x^2 +3x +5=0 one root being 1-2i.

If x=2 and x=3 are roots of the equation 3x^(2)-mx+2n=0 , then find the values of m and m.

If both roots of the equation x^(2)-(m-3)x+m=0(m epsilonR) are positive, then

If x=2 and x=3 are roots of the equation 3x^2-2k x+2m=0, find the value of k and m .